Wave dispersion under finite deformation

► Exact finite-strain dispersion relations are derived for wave motion in thin rods and beams. ► Derivations asymptotically converge to infinitesimal-strain dispersion relations at low frequencies and wave amplitudes. ► Results are relevant to problems involving large elastic motion such as waves produced by cracks and dislocations. ► Results demonstrate importance of incorporation of longitudinal-transverse motion coupling in nonlinear analysis of thin structures. ► Proposed approach can incorporate nonlinear constitutive laws and be extended to multi-dimensional media.